Question

Among a group of 60 engineering students, 24 take math and 29 take physics. Also 10 take both physics and statistics, 13 take both math and physics, 11 take math and statistics, and 8 take all three subjects, while 7 take none of the three. a) How many students take statistics? b) What is the probability that a student selected at random takes all three, given he takes statistics?

Answer 1

Answer:

a) 26

b) 0.3076                

Step-by-step explanation:

We are given the following in the question:

M: Math

P: Physics

S: Statistic

n(Math) = 24

n(Physics) = 29

$n(P\cap S) = 10$

$n(M\cap P) = 13$

$n(M\cap S) = 11$

$n(M\cap P\cap S) = 8$

$n(M'\cap P'\cap S') = 7$

a) Number of students who take statistics

Formula:

$n(P\cup M\cup S)=\\n(P)+n(M)+n(S)-n(P\cap M)-n(P\cap S)-n(M\cap S)+n(P\cap M\cap S)$

Putting the values, we get,

$n(P\cup M\cup S) = n - n(P'\cap M'\cap S') = 60-7 = 53$

$53 = 24 + 29 + n(S) -10-13-11+8\\n(S) = 53-24-29+10+13+11-8\\n(S) = 26$

Thus, 26 students took statistic.

b) probability that a student selected at random takes all three, given he takes statistics

$p(\text{All three subject}|\text{Statistic})\\\\=\displaystyle\frac{n(P\cap M\cap S)\cap n(S)}{n(S)}\\\\= \frac{8}{26} = 0.3076$